Solve -xyz*9xyz^2/(-6x)^2y^0z^7

$$\frac { - x y z \times 9 x y z ^ { 2 } } { ( - 6 x ) ^ { 2 } y ^ { 0 } z ^ { 7 } }$$

Evaluate

$$-\frac{y^{2}}{4z^{4}}$$

Short Solution Steps

Multiply y and y to get y^{2}.

$$\frac{\left(-x\right)y^{2}z\times 9xz^{2}}{\left(-6x\right)^{2}y^{0}z^{7}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(-x\right)y^{2}z^{3}\times 9x}{\left(-6x\right)^{2}y^{0}z^{7}}$$

Cancel out z^{3} in both numerator and denominator.

$$\frac{9\left(-x\right)xy^{2}}{y^{0}\left(-6x\right)^{2}z^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{9\left(-x\right)xy^{2}}{\left(-6x\right)^{2}z^{4}}$$

Expand \left(-6x\right)^{2}.

$$\frac{9\left(-x\right)xy^{2}}{\left(-6\right)^{2}x^{2}z^{4}}$$

Calculate -6 to the power of 2 and get 36.

$$\frac{9\left(-x\right)xy^{2}}{36x^{2}z^{4}}$$

Cancel out 9x in both numerator and denominator.

$$\frac{\left(-x\right)y^{2}}{4xz^{4}}$$

Factor the expressions that are not already factored.

$$\frac{-xy^{2}}{4xz^{4}}$$

Cancel out x in both numerator and denominator.

$$\frac{-y^{2}}{4z^{4}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{y^{2}}{-4z^{4}}$$

Differentiate w.r.t. y

$$-\frac{y}{2z^{4}}$$